174 IMPACT AGAINST ANT SURFACE OF REVOLUTION. 



the water projected per second = awv, and therefore the 

 work per second 



that is, the work varies as the cube of the velocity of the 

 water. 



. COR. Let = the coefficient of velocity; then, from (1) 

 of Art. 93, we have 



v = <(>\/%gh, 



which in (1) gives 



work per second = <j) 3 awhV%gh. (2) 



99. Impact of a Stream of Water against any 

 Surface of Revolution. Let BAG be a surface of revo- 

 lution, against which a stream of 

 water FA, moving in the direction 

 of the axis AP of the surface, im- 

 pinges. Let W be the weight of 

 water discharged on the surface per 

 second, v its velocity, v t the veloc- 

 ity of the surface, and the angle 

 BTP which the tangent HT to the 

 surface at B makes with the axis 

 AP, or which each filament HB of the stream of water, on 

 leaving the surface, makes with the direction of the axis BD. 

 Then the water impinges upon the surface with the velocity 

 v v 1 ; and, if friction be neglected, the water passes over 

 the surface with that velocity, and leaves it in a tangential 

 direction, TH, TK, etc., with the same velocity. From 

 the tangential velocity BH = v v l , and the velocity BD 

 = ?>j of the surface parallel to the axis, we have the result- 

 ant velocity BE = V of the water, after it has impinged 

 on the surface, by the formula for the parallelogram of 

 velocities, 



